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Answer: 0.6594
## Explanation The standard error of the regression (SER), also known as the standard error of the estimate (SEE), is calculated using the formula: $$\text{SER} = \sqrt{\frac{\text{SSR}}{n - (k + 1)}}$$ Where: - SSR = Sum of Squared Residuals = 20 - n = number of observations = 50 quarters - k = number of independent variables = 3 (P/Sales, P/E, and P/B) Plugging in the values: $$\text{SER} = \sqrt{\frac{20}{50 - (3 + 1)}} = \sqrt{\frac{20}{50 - 4}} = \sqrt{\frac{20}{46}} = \sqrt{0.4347826} = 0.6594$$ **Key points:** 1. The degrees of freedom for the regression is n - (k + 1), where k+1 accounts for all parameters estimated (k slope coefficients + 1 intercept) 2. SSR represents the unexplained variation in the regression 3. The R² value of 90.12% is not needed for this calculation 4. The p-values and coefficients are also not needed for this calculation This matches option A: 0.6594
Author: Nikitesh Somanthe
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A hedge fund manager runs a regression for quarterly returns on a stock over 50 quarters against three independent variables P/Sales, P/E, and P/B. He generates the following results:
| Variable | Coefficient | p-Value |
|---|---|---|
| Intercept | 9.02 | 0.10 |
| P/Sales | 1.20 | 0.16 |
| P/E | 4.12 | 0.19 |
| P/B | 2.34 | 0.21 |
| R² | 90.12% |
The hedge fund manager has computed the sum of squared residual errors (SSR) as 20. What is the value of the standard error of the regression (SER)?
A
0.6594
B
0.6523
C
0.9012
D
0.9158